Directions Vectors, Grade 11 physics
I/ Directions

There are many acceptable methods of writing vectors. As long as the vector has a magnitude and a direction, it is most likely acceptable. These different methods come from the different methods of expressing a direction for a vector.

1/ Relative Directions
The simplest method of expressing direction is relative directions: to the left, to the right, forward, backward, up and down.

2/ Compass Directions
Another common method of expressing directions is to use the points of a compass: North, South, East, and West. If a vector does not point exactly in one of the compass directions, then we use an angle. For example, we can have a vector pointing 40◦ North of West. Start with the vector pointing along the West direction: Then rotate the vector towards the north until there is a 40◦ angle between the vector and the West.


3/ Bearing
The final method of expressing direction is to use a bearing. A bearing is a direction relative to a fixed point. Given just an angle, the convention is to define the angle with respect to the North. So, a vector with a direction of 110◦ has been rotated clockwise 110◦ relative to the North. A bearing is always written as a three digit number, for example 275◦ or 080◦ (for 80◦).

Exercise: Scalars and Vectors
E - 1. Classify the following quantities as scalars or vectors:

1.1 12 km
1.2 1 m south
1.3 2 m·s$^{−1}$, 45◦
1.4 075◦, 2 cm
1.5 100 km·hr$^{−1}$, 0◦

E - 2. Use two different notations to write down the direction of the vector in each of the following diagrams:

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Physics 11.I Mathematics of Vectors

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